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In this paper, it is shown that spatial distributions in the field-sweep rate and in the contact resistances along the length of Rutherford-type superconducting power cables provoke a nonuniform current distribution during and after a field sweep. This process is described by means of boundary-induced coupling currents (BICCs) flowing through the strands over lengths far larger than the cable pitch. The dependence of the BICCs on the cable parameters (geometry, contact resistances etc.) is investigated by modelling the cable by means of a comprehensive network model. Working formulae are presented that give a first estimate of the characteristic time, the amplitude, and the characteristic length of the BICCs in any kind of magnet wound from a Rutherford-type cable. The results of these calculations show that BICCs can attain large values in multistrand cables, and hence play an important role in the ramp-rate limitation and field quality of high-field accelerator magnets even if the field-sweep rate is small.